16" oc allows even spacing on 48" panel intervals, and its just about the minimum space that some contractors can fit through without snagging their belt buckle.
The spacing of wall studs is dependent on the load they are carrying. Spacings of 16", 12" & 8" are very common for load bearing walls. Non-load bearing wall studs are usually spaced at 24" o.c so that the wall panel edges terminate at a stud.
" Light Frame House Construction " US Office of Education 1940 Reprint " the standard length of lath has established 16" as the standard spacing for studs " ..... "A Museum of Early American Tools" Eric Sloane p 32-33 illustrates the making , with a froe, of "accordian lath" where an oak slab is partially split on alternating sides and pulled apart like an accordian !....Wood lath uses green wood and is thouroughly wet before use so the wood doesn't absorb water from the plaster.So a convenient width of wood for the accordian lath was 16" ,that established 16" stud distance which became standard .
Actually, going back further to ancient Britannia, prior to the invention of the measuring rule, the standard of measure was the length of the forearm, or about 16". Hence, the 16" standard.